A model of the Villa Foscari (La Malcontenta) at the Royal Academy's Andrea Palladio exhibition. Photograph: Nils Jorgensen/Rex Features

If the great Renaissance architect Andrea Palladio were alive today, what would he be designing? Would the grandaddy of western architecture still be doing classical buildings, or would he be working in a more stripped-down style? Would he side with, say, Prince Charles or Norman Foster? On one level it's a fanciful question, but 428 years after his death, Palladio's legacy – along with classical architecture in general – is still passionately debated. One side claims that classicism is the language of history and popular taste, and that we should therefore continue using it; the other sees it as anachronistic, redundant, connected to outdated values. The opening of a major new Palladio exhibition looks set to stir up this ages-old dispute once more.

The funny thing is, architects of every shade are keen to claim him as one of theirs. "Just you wait," says architect Robert Adam. "There'll be a great flush of them at the exhibition. Richard Rogers will say, 'I'm really a Palladian' and so will Norman Foster. The modernists will say it's all about proportion and rhythm and so on.

"This is the way people who aren't the least bit interested in history claim they are connected to it. They take it and they abstract it in such a way that no one, save for them and their mates, would actually recognise it."

Adam, lest there be any doubt, is what you'd call a traditionalist. His firm is the largest in Europe dealing with what he calls "progressive classical design". That could mean anything from grand country houses to technologically up-to-date office blocks, all rendered in the classical vocabulary of columns and capitals, porticoes and pediments. In other words, the vocabulary that Palladio himself translated from the ruins of ancient Rome and applied to the villas of wealthy Venetian landowners in the 16th century, and which his famed Quattro Libri dell'Architettura (Four Books of Architecture) taught other architects how to use. Although classical forms had been reinterpreted before, the decisive split came in the early 20th century, when these historical forms were stripped down or simply discarded by modernist revolutionaries like Le Corbusier, Mies van der Rohe and Walter Gropius in favour of a simpler, purer language that reflected the spirit of the age and the possibilities opened up by concrete, steel and glass.

Even so, the modernists still took their cue from Palladio. Comparisons can be made between the floor plans of Le Corbusier's best-known villas and those of Palladio, for example, and contemporary architects argue there's much more to Palladio's work than just the classical details. "Obviously there's the geometry and proportions," says Chris Wilkinson, of Wilkinson Eyre architects, who once took his whole office to see Palladio's work in the flesh. "But the other thing that resonates with me is the elegant simplicity of [Palladio's] buildings. A lot of it is very, very plain. And they're actually quite functional and economical. For example, I was terribly impressed to hear that the very fine ramp that leads you up to the piano nobile at the Villa Emo, was not only designed so that you could ride up to the front porch on horseback, but also doubles up as a threshing surface in harvest time. That just seemed to me so practical."

A Quinlan Terry building on Baker Street. Photograph: David Sillitoe/Guardian

Nevertheless, the traditionalists are fighting back – and gaining ground, they say. Last September, at the Prince of Wales's Foundation, another exhibition was held to mark Palladio's 500th birthday, entitled New Palladians. This brought together the work of classically oriented architects from around the world, with a view to "establishing a credible counterpoint to the constant erosion of cornerstones of traditions in architecture and building", as the organisers put it. All the usual suspects were represented, including Adam, Quinlan and Francis Terry, and Leon Krier, the guiding hand behind Poundbury village in Dorset. The projects ranged from pastiche country mansions to historically sensitive town plans; the catalogue, it has to be said, resembled that of an upmarket property agent.

One of the key organisers of the exhibition was Alireza Sagharchi, secretary of the Traditional Architecture Group, an affiliation of like-minded architects. He likens the classical language to the English language, and argues that we can still understand a Victorian or Georgian novel today precisely because we haven't reinvented it from scratch. "The way we structure a building to convey a certain set of values hasn't changed, and we don't see why it should change," says Sagharchi.

"That's how you maintain continuity and tradition; those are the values we are communicating. We think they are fundamental to our survival."

You could say there's room for both in our pluralistic world, but – at least in their view – the traditionalists have been pushed out. "Although many modernists will say that people can do what they like," says Adam, "they sort of don't want us."

Adam believes that change is in the air, however. He predicts that the current recession will spell the end of modern skyscrapers and wacky noughties shapes, which have come to represent the hubristic building culture of the last few years, just as tellingly as the recession of the 1990s destroyed the appeal of postmodern architecture. Buildings such as the Gherkin and Manchester's Beetham tower will soon look as outmoded as those 1980s relics, say the classicists. Instead, the public will want the safe, solid message that only traditional architecture can provide. The thread that was broken in the 20th century will be picked up again, the argument runs, and modernism will be seen as an isolated moment of madness.

But the divide between the two is no longer clear-cut. Modernism with a capital M is not what it was. Even diehard modernists will concede that the movement's original approaches to town planning – wide, straight boulevards and orderly mega-blocks of housing – were hopelessly wrong. Now they are more likely to plan towns or villages in ways that the classicists would recognise.

And even those who have sought a new architectural language, one that moves beyond the whole classical/modernist debate, still claim Palladio as an influence. This summer, Zaha Hadid's firm created two indoor installations at Palladio's Villa Foscari: complex, swirling sculptures that were based on the harmonic proportions of the villa's interior. This is exactly the sort of abstracted, ahistorical style Adam bemoans. But Patrik Schumacher, a partner at Hadid's firm, believes it is the style Palladio would adopt if he were alive today. "The social diagram of the villa was heightened into this sublime, crystalline geometric order in Palladio's buildings," he says. "We try to do something similar. We are equally obsessed with the idea of a viscerally felt order."

The idea that Zaha Hadid is Palladio's rightful heir would no doubt horrify Robert Adam and his ilk but, as Schumacher points out, Palladio was a great innovator in his time. Just as he was a faithful devotee and custodian of classical values, he was an intuitive aesthete and craftsman and a shrewd operator with a gift for expressing the social position of his wealthy clients. So maybe it's not so strange a leap to imagine Palladio trying his hand at computer-aided design after all.